I am currently going through an application for an IVA. I am wondering if I can save money within the monthly amount that has been set by my IP? And if I can save it, am I allowed to set up an Help To Buy ISA and put the savings into that? Is that allowed as part of the IVA?

You can save money from your allowances if you can. Not sure about the ISA though as you will be unable to buy a property whilst in the IVA.
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Sharing from experiences of dealing with debt
The greatness of a man is not in how much wealth he acquires, but in his integrity and his ability to affect those around him positively.
Bob Marley.http://kallis3.blogs.iva.co.uk

If you consistently save, say, £50 a month to an ISA, creditors will be wondering why they can't be getting that instead and might want your expense allowances reviewed. Whilst saving modest amounts from your share of overtime and expenses, maybe the odd small windfall, is to be encouraged, regular savings will be looked at with different eyes.